If, on the other hand, you feel your landlord is mis handling your mail in anyway then I would report it to the postal service. But to seek legal counsel for something like this would cost you a lot of money and would probably not gain you anymore than if you had gone to the postal service yourself.
It would be illegal for him to "open" your mail, but it sounds as though he's just being nice. Since it's a communal mailbox, if you were to get to it first, you'd have to "go through the mail", too.
If you'd prefer for the landlord, once he's gone through and found his own mail, to leave yours in the communal mailbox, then you should just tell him. I'm sure he'd be totally surprised to find out that his act of kindness is making you uncomfortable.
I suggest that you speak with your landlord about the communal mailbox and express your thoughts.
Perhaps request your own mailbox. Never hurts to ask :)
And you need to consult an attorney to find out the answer if it's legal to share a mailbox.
Good luck to you!
Prudential Connecticut Realty